1.

Let `a,x,b` be in `A.P`, `a,y,b` be in `G.P` and `a,z,b` be in `H.P`. If `x=y+2` and `a=5z`, thenA. `y^(2)=xz`B. `x gt y gt z`C. `a=9`, `b=1`D. `a=1//4`, `b=9//4`

Answer» Correct Answer - A::B::C
`(a,b,c)` `2x=a+b`
`y^(2)=ab`
`z=(2ab)/(a+b)`
`x=y+2`
and `a=5z`
`z=(2y^(2))/(2x)`
`impliesy^(2)=xz`
`x=y+2`
`:.(a+b)/(2)=sqrt(ab)+2`………`(i)`
and `a=5((2ab))/(a+b)`
`implies(a+b)=10b`
`impliesa=9b`
`:.` from `(i) (9b+b)/(2)=sqrt(9b^(2))+2`
`implies5b=3b+2`
`impliesb=1`
So `a=9`
`implies x gt y gt z`


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